Question

If $R_{1}$ and $R_{2}$ are respectively the filament resistances of a $200\, W$ bulb and a $100\, W$ bulb designed to operate on the same voltage.

• A. $R_{1}$ is two times $R_{2}$
• B. $R_{2}$ is two times $R_{1}$
• C. $R_{2}$ is four times $R_{1}$
• D. $R_{1}$ is four times $R_{2}$

Answer 1

Answer: (B)

If $V$ is the voltage rating of the two bulbs then their resistances are given as
$R =\frac{V^{2}}{P_{2}}=\frac{V^{2}}{200} $
and $R_{2}=\frac{V^{2}}{P_{1}}=\frac{V^{2}}{100} $
$\Rightarrow R_{2}=2 R_{1}$